The existence of doubly near resolvable (v,3,2)‐BIBDs | Zendy

Lamken E. R. | Zendy

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The existence of doubly near resolvable (v,3,2)‐BIBDs

Author(s) -

Lamken E. R.

Publication year - 1994

Publication title -

journal of combinatorial designs

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.618

H-Index - 34

eISSN - 1520-6610

pISSN - 1063-8539

DOI - 10.1002/jcd.3180020606

Subject(s) - mathematics , combinatorics , block (permutation group theory) , spectrum (functional analysis) , class (philosophy) , block size , physics , ecology , quantum mechanics , artificial intelligence , key (lock) , computer science , biology

The existence of doubly near resolvable ( v ,2,1)‐BIBDs was established by Mullin and Wallis in 1975. In this article, we determine the spectrum of a second class of doubly near resolvable balanced incomplete block designs. We prove the existence of DNR( v ,3,2)‐BIBDs for v ≡ 1 (mod 3), v ≥ 10 and v ∉ {34,70,85,88,115,124,133,142}. The main construction is a frame construction, and similar constructions can be used to prove the existence of doubly resolvable ( v ,3,2)‐BIBDs and a class of Kirkman squares with block size 3, KS 3 ( v ,2,4). © 1994 John Wiley & Sons, Inc.

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